博文视点有奖答题第二题：青蛙跳台阶问题

博文视点有奖答题第二题：青蛙跳台阶问题
（1）一只青蛙一次可以跳上 1 级台阶，也可以跳上2 级。求该青蛙跳上一个n 级的台阶总共有多少种跳法。（2）一只青蛙一次可以跳上1级台阶，也可以跳上2 级……它也可以跳上n 级，此时该青蛙跳上一个n级的台阶总共有多少种跳法？
#include <stdio.h>#include <stdlib.h>int main(int ac, int* av[]){int num_steps, result;printf("Please input the num of steps\n");scanf("%d", &num_steps);result = 0;result += cal_steps(num_steps);printf("There are %d ways for the frog to pass %d steps.\n", result, num_steps);}int cal_steps(int n){int i, j, *a;a = (int*)malloc(n * sizeof(int));a[0] = 1;a[1] = 2;for(i=2; i<n; i++){for(j=0; j<i; j++)a[i] += a[j];a[i] += 1;}return a[n-1];}int cal_steps_two(int n){int i, pre, result, tmp;if(n == 1) return 1;if(n == 2) return 2;if(n > 2){pre = 1;result = 2;for(i=2; i<n; i++){tmp = result;result = result + pre;pre = tmp;}}return result;}int cal_steps_recursive(int n){int steps;steps = 0;if((n == 0) || (n < 0)){return 0;}if(n == 1)return 1;if(n == 2)return 2;if(n > 2){steps += cal_steps(n-1) + cal_steps(n-2);}return steps;}